Page 234 - Structural Steel Designers Handbook AISC, AASHTO, AISI, ASTM, and ASCE-07 Design Standards

Brockenbrough_Ch05.qxd 9/29/05 5:12 PM Page 5.14

CRITERIA FOR BUILDING DESIGN

5.14 CHAPTER FIVE

For singly symmetric members where y is the axis of symmetry,

 F + F   4 FF H 
ey ez
F =   ey 2 H ez  1 − 1 − ( F + F ) 2    (5.26)

e


ey
ez
For unsymmetric members, F e is the lowest root of the cubic equation,
 x  2  y  2
−
(F − F ex )(F − F ey )(F − F ez ) F e 2 (F − F ey )   r   − FF − F ex )   r   = 0 (5.27)
o
o
2
(
e
e
e
e
e
e
o
o
The following definitions apply:
K z = effective length factor for torsional buckling
G = shear modulus of elasticity of steel = 11,200 ksi (77,200 MPa)
6
6
C w = warping constant, in (mm )
4
4
J = torsional constant, in (mm )
4
4
I x , I y = moment of inertia about the principal axes, in (mm )
x o , y o = coordinates of shear center with respect to the centroid, in (mm)
r o = Polar radius of gyration about shear center, in (mm)
I + I
r = x + y + x y (5.28)
2
2
2
o o o
A
x + y 2
2
H =− o o (5.29)
1
r o 2
π 2 E
F = (5.30)
ex
( KL r / ) 2
x
x
π 2 E
F = (5.31)
ey
( KL r / ) 2
y
y
π 2 EC  1
F =  w + GJ  (5.32)
ez
 ( KL) 2  Ar o 2
z
2
For doubly symmetric I-shaped sections, C w may be taken conservatively as I y d /4. For tees and
double angles, take C w and x o as 0.
5.4.3 Compressive Strength of Single-Angle Members
The compressive strength of single-angle members can be determined from Eqs. (5.19)–(5.21), using
KL/r as given in this article and neglecting eccentricity, provided the angles are (1) loaded at the ends
in compression through the same one leg, (2) attached by welding or by two-bolt-minimum connec-
tions, and (3) subjected to no intermediate transverse loads. For other conditions, see the AISC
Specification. The modified slenderness ratios are intended to account indirectly for bending due to
eccentricity of loading and end restraint from truss chords.
For equal-leg angles, or unequal-leg angles connected through the longer leg, which are individ-
ual members or are web members of planar trusses with adjacent web members attached to the same
side of the gusset plate or chord:
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